Goal-oriented adaptive finite element methods with optimal computational complexity

01/27/2021
by   Roland Becker, et al.
0

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design a goal-oriented adaptive finite element method (GOAFEM), which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method (PCG). We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates with respect to the number of degrees of freedom as well as the computational cost.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/13/2021

Goal-oriented adaptive finite element method for semilinear elliptic PDEs

We formulate and analyze a goal-oriented adaptive finite element method ...
research
12/01/2022

Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs

We consider a general nonsymmetric second-order linear elliptic PDE in t...
research
07/21/2020

A note on energy contraction and optimal convergence of adaptive iterative linearized finite element methods

In this note, we revisit a unified methodology for the iterative solutio...
research
05/22/2020

A short note on plain convergence of adaptive least-squares finite element methods

We show that adaptive least-squares finite element methods driven by the...
research
07/22/2022

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Given a partial differential equation (PDE), goal-oriented error estimat...
research
03/24/2020

On the threshold condition for Dörfler marking

It is an open question if the threshold condition θ < θ_ for the Dörfler...
research
04/27/2020

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

We consider a second-order elliptic boundary value problem with strongly...

Please sign up or login with your details

Forgot password? Click here to reset